The heat kernel for deformed spheres

TL;DR

This paper derives the heat kernel expansion for Laplace operators on deformed spheres, revealing how deformations affect coefficients and cancel conformal anomalies in certain higher-dimensional spaces.

Contribution

It provides explicit calculations of heat kernel coefficients on deformed spheres and shows anomaly cancellation under specific deformations.

Findings

Heat kernel coefficients depend on deformation parameters

Conformal anomaly can be canceled through specific deformations

Explicit formulas for 2D and 3D deformed spheres

Abstract

We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation parameters. We find that under some deformation the conformal anomaly for free scalar fields on $R^4\times \tilde S^2$ and $R^6\times \tilde S^2$ is canceled.